AI 中文总结
本研究将结构化多尺度代数多重网格（SM-AMG）的代数变体AM-AMG应用于格点场论，在两味施温格模型中与DDαAMG基准测试，发现细网格下两者计算成本相当但AM-AMG迭代更多，粗网格下AM-AMG去除低模存在困难。
AI 中文摘要
格点量子色动力学（Lattice QCD）中用于狄拉克方程的最先进求解器基于自适应多重网格方法，这些方法需要对大量算法参数进行微调以实现最优性能。我们将一种从油藏模拟中改编而来的新型多重网格方法——结构化多尺度代数多重网格（Structured-Multiscale Algebraic Multigrid，SM-AMG）应用于格点场论，该方法通过构建带有重叠边界的紧凑聚合体来粗化网格并生成精确的插值。其关键优势在于聚合体尺寸是主要可调参数。在我们的结果中，我们采用了SM-AMG的代数变体，称为聚合多尺度代数多重网格（Aggregative-Multiscale AMG，AM-AMG）。我们将AM-AMG的效率与DDαAMG（一种成功缓解临界慢化效应的自适应多重网格求解器）进行基准测试，在两味施温格模型（two-flavor Schwinger model）框架内使用威尔逊离散化方案对两种求解器进行比较。在细网格上，两种方法在临界点附近及大体积下的运算量相似，反映出相当的计算成本；但AM-AMG的细网格迭代次数更多。在粗网格上，AM-AMG在去除接近临界质量的低模时遇到困难。
英文摘要
State-of-the-art solvers for the Dirac equation in Lattice QCD are based on adaptive multigrid methods. These require fine-tuning of many algorithmic parameters to achieve optimal performance. We apply a new multigrid approach to Lattice Field Theory adapted from oil-reservoir simulations: Structured-Multiscale Algebraic Multigrid (SM-AMG). This method builds compact aggregates with overlapping borders to coarsen the grid and yields accurate interpolation. A key advantage is that aggregate size is the primary tunable parameter. For our results, we used SM-AMG in an algebraic approach, called Aggregative-Multiscale AMG (AM-AMG). We benchmark the efficiency of AM-AMG against that of DD$α$AMG, a successful adaptive multigrid solver which alleviates critical slowing down. The two solvers are compared within the framework of the two-flavor Schwinger model using the Wilson discretization. On fine lattices, the operation count of both methods is similar near the critical point and for large volumes, reflecting a comparable computational cost. However, the number of fine-grid iterations is larger for AM-AMG. On coarse lattices, AM-AMG encounters difficulties to remove the low modes close to the critical mass.
Comments16 pages, 7 figures, 2 algorithms, 4 tables, submitted to Computer Physics Communications
